Alarm going off every time I take key out of ignition or turn switch on. This just started today and I have never had this problem before. The car is a 2009 and I have had it for one month.

You have bade contact in the ignition switch .

Sounds to me like you need a new ignition switch. Take the vehicle to a mechanic and have them further evaluate.

Some cars do this if the battery level is low. I had a Chevy Impala that when the battery was low you could not get the key out of the ignition. Hooked up jumpers and it was fine. The newer cars need a really good battery all the time.

if the key itself doesnt turn its not an alarm issue its the ignition switch itself u need to replace it, it is worn out

The steering lock may be binding the ignition lock cyl preventing the key from turning or the key may be worn out. Try turning the steering wheel back and forth while wiggling and turning the ignition key. To get the alarm to turn off without starting the car try locking and unlocking the vehicle from the passenger side door. There is a micro switch on the drivers side door lock cyl that may be bad and preventing the alarm from dis arming. This is all providing it is a toyota factory alarm sys.

put key in door lock,unlock/hold key over windows will go down....then lock/hold key over,windows will go up,press and hold unlock button on remote for 30 secs,you have just reset the alarm/immobiliser.

System operation
System arms 5 seconds after switching ignition OFF. Switch ignition ON. Ensure clock LED illuminates for 3-5 seconds. If LED flashes rapidly at regular intervals for approximately 1 minute, then flashes at irregular intervals: Key code not recognised. Remove key and try again.
Programming
When
System malfunction: LED illuminates for 1 minute, then flashes at irregular intervals. Key(s) added or replaced.
NOTE: Replacement keys MUST have blue mark. Keys with red mark are NOT compatible with this system.
How
NOTE: Programming method using vehicle keys can be deactivated using diagnostic equipment.
Obtain 2 programmed keys (A and B). Insert key A into ignition switch. Turn ignition switch to position II. Wait 1 second. Switch ignition OFF. Remove key A. Insert key B into ignition switch within 5 seconds. Turn ignition switch to position II. Wait 1 second. Switch ignition OFF. Remove key B. Within 10 seconds: Insert key to be programmed into ignition switch. Turn ignition switch to position II. Wait 4 seconds. Switch ignition OFF. Wait 5 seconds. Start engine. If engine does not start and clock LED flashes: Switch ignition ON. Wait at least 20 seconds. Switch ignition OFF. Repeat programming procedure. Repeat above procedure to program remaining keys. Keys can also be programmed using diagnostic equipment

do you have a remote door opener fob,try locking and unlocking doors with it

Get a new ignition key switch, and ignition key. No, it won't be cheap.
With the key switch messing up, it causes problems with the alarm system.

(And you know what problems the alarm system is causing)

sounds like you have an aftermarket alarm not factory most of these alarma are equipped with a starter interupt that will not vehicle start. when connecting the battery ist is normal for the alarm to sound some alarms may not sound if ignition is on while connecting battery, however this is not reccomended. after connecting battery and alarm sounds you should be able to turn it off with trasmitter, if you do not have one then you will need to put key in ignition turn it on and look under the dash for a valet switch or togle switch this may override the alarm and let car start if you cannot locate this you can alway locate the alarm box under dash and unplug it as last resort most alarm defaults will let the car start when this is done. hope this helps